The partial copula provides a method for describing the dependence between two random variables X and Y conditional on a third random vector Z in terms of nonparametric residuals U₁ and U₂. This paper develops a nonparametric test for conditional independence by combining the partial copula with a quantile regression based method for estimating the nonparametric residuals. We consider a test statistic based on generalized correlation between U₁ and U₂ and derive its large sample properties under consistency assumptions on the quantile regression procedure. We demonstrate through a simulation study that the resulting test is sound under complicated data generating distributions. Moreover, in the examples considered the test is competitive to other state-of-the-art conditional independence tests in terms of level and power, and it has superior power in cases with conditional variance heterogeneity of X and Y given Z.